Metering the mass flow rate of a gas is important for many industrial processes. In the case of the semiconductor industry, metering must be especially accurate, because deviations in the flow rate of only several percent can lead to process failures.
The industry-standard flow control device is a mass flow controller (MFC) containing a flow restriction in the form of a valve that can be partially opened to allow increased flow or partially closed to decrease flow. The opening of the valve is controlled by a closed loop feedback circuit that minimizes the difference between an externally provided set point and the reading from an internal flow measuring device. The flow measuring device uses a thermal sensor with two resistance-thermometer elements wound around the outside of a tube through which the gas flows. The elements are heated by applying an electric current. As the gas flows through the tube, it picks up heat from the first element and transfers it to the second element. The resulting temperature differential between the two elements is a measure of the mass flow rate of the gas. In the newer, pressure insensitive MFCs, a pressure transducer is included between the thermal sensor and the control valve to account for the effects of changing pressure on flow.
When the flow of gas through the MFC is changing, the thermal sensor will not be in a steady state condition. Furthermore, the thermal sensor requires some amount of time, typically 0.5 to 3 seconds, after the flow has stopped changing, to attain a steady state temperature difference between the two elements. As a result of this behavior, when the MFC is commanded to move to a certain flow set point, there will be a period of time during which the flow is not at the desired value. In some MFCs, the flow increases monotonically to the set point; in other MFCs, there can be significant overshoot of the flow rate before it settles to its desired level. The flow behavior during this period of time when the flow has not yet settled to its desired value is referred to as the “transient” response of the MFC.
Manufacturers of MFCs focus heavily on making certain that steady state flows are as accurate as possible. The only significant attention paid to the transient response is its duration. The “settling time” specification of an MFC is the maximum time required for the MFC to settle to within some percentage of its desired flow rate. Nevertheless, with process requirements, especially in the semiconductor industry, becoming more demanding, and processes frequently being only seconds long, the transient response of MFCs is becoming increasingly important.
Measurement of the transient response, however, has been challenging. Various techniques exist to measure steady state flows with a high level of accuracy. For example, a rate of rise (or rate of drop) measurement is performed by flowing gas through the MFC into (or out of) a known volume and measuring the pressure rise (or drop) in the volume. The actual flow rate can be determined by calculating the rate of pressure rise or drop and using established pressure-temperature-volume gas relations to calculate the number of moles of gas flowing through the MFC.
Another method for measuring flow rate is that of measuring the pressure drop across a flow restriction, where the flow restriction is placed either upstream or downstream of the MFC. With a relationship established a priori between the pressure drop across the flow restriction and the flow through the flow restriction, the flow through the MFC can be determined.
Unfortunately, these measurement techniques typically require a measurement time that is very long compared to the transient response. A rate of rise measurement, for example, can take as long as a minute, especially for the lower flow rates, such as 1 sccm (standard cubic centimeters per minute). In addition, these measurements frequently change either the upstream or downstream pressure during the transient response of the MFC. This changing pressure can influence the response of the MFC, making it unclear as to what is the true transient response of the MFC and what is being observed only as a result of the way in which the measurement is being made.
The shortcomings of current flow measurement techniques for measurement of MFC transient responses, especially with the accuracy and time resolution that is desired, illustrate why an improved gas flow transient measurement scheme is desirable.
Key requirements for gas flow transient measurements are the following:                a sufficient time resolution, such as tens of milliseconds        an accuracy of approximately 1% of the actual flow        no perturbation of the pressure upstream of the MFC under test        no perturbation of the pressure downstream of the MFC under test.        